124 Experiment with conductor of any form 



ratio of the distances without its having been perceived in this experiment, 

 let AT be a diameter of the two concentric spheres ABD and abd, and let 

 A a be bisected in e. Ae in this experiment was about -35 of an inch and 

 Te 13-1 inches, therefore if the electric attraction and repulsion is inversely 

 as the 2 + ^'jjth power of the distance, it may be shewn that the force 

 with which the redundant fluid in ABD repels a particle at e towards the 

 center is to that with which the same quantity of fluid collected in the 

 center would repel it in the contrary direction as I to 57. 



But as the law of repulsion differs so little from the inverse duplicate 

 ratio, the redundant fluid in the inner globe will repel the point e with 

 very nearly the same force as if it was all collected in the center, and 

 therefore if the redundant fluid in the inner globe is J 7 th part of that in 

 ABD the particle at e will be in equilibrio, and as e is placed in the middle 

 between A and a, there is the utmost reason to think that the fluid in the 

 whole wire A a will be so too. We may therefore conclude that the electric 

 attraction and repulsion must be inversely as some power of the distance 

 between that of the 2 + ^th and that of the 2 ^th, and there is no 

 reason to think that it differs at all from the inverse duplicate ratio*. 



235] EXPERIMENT II. A similar experiment was tried with a piece of 

 wood 12 inches square and 2 inches thick, inclosed between two wooden 

 drawers each 14 inches square and 2 inches deep on the outside, so as to 

 form together a hollow box 14 inches square and 4 thick, the wood of 

 which it was composed being -5 to -3 of an inch thick. 



The experiment was tried in just the same manner as the former. I 

 could not perceive the inner box to be at all over or undercharged, which 

 is a confirmation of what was supposed at the end of Prop. IX [Art. 41] 

 that when a body of any shape is overcharged, the redundant fluid is 

 lodged entirely on the surface, supposing the electric attraction and re- 

 pulsion to be inversely as the square of the distance f. 



DEMONSTRATION OF COMPUTATIONS IN [ART. 234]. 



Let aef be a sphere, c its center, b any point within it, af a diameter, 

 plane perpendicular to af. 



Let cb = a, ba = d, bf = s and ad = #, and let the 

 repulsion be inversely as the n power of the distance. 

 The convex surface of the segment Eae is to that of 

 the whole globe as ad : af, and therefore if the point d 

 is supposed to flow towards/, the fluxion of the surface 

 Eae is proportional to x, and the fluxion of its re- 

 pulsion on b in the direction dc is proportional to 



Ee any 



* [Note 19, p. 404.] 



t [Art. 561.] 



